Download Uniform Circular Motion

Name___________________________
PHY1
Uniform Circular Motion
Purpose: To determine the speed, centripetal acceleration, and centripetal force for a mass undergoing
uniform circular motion.
Materials: You will need a glass tube wrapped in masking tape, 1.5 m length piece of string, rubber
stopper, mass hanger, slotted masses, stopwatch, and meter stick.
Background: An object in uniform circular motion with a radius (r) travels in a circle at a constant
speed. Although the speed is constant, the velocity is changing since the mass’s direction of travel is
continuously changing. Based on Newton’s second law, we know that where there is acceleration
there must be a force. The speed (v) of the mass is simply the distance it travels per unit time. The
distance is the circumference of the circle and the time to complete one revolution is the period (T).
The speed can therefore be determined using Equation 1. We will use a string attached to a hanging
mass to supply the centripetal force (Fc) which causes the mass to move in a circle. The tension of the
string is directed toward the center of the circular path. From Newton’s second law, we know that the
force and acceleration have to be in the same direction; therefore the centripetal force must be directed
toward the center of the circular as well. The mathematical relationships for the net centritpetal force
and acceleration are shown in Equations 2 and 3.
v=
2
ac = Vr
2πr
t
(1)
(2)
2
Σ Fc =
mV
r
(3)
Procedure: Secure a rubber stopper to one end of a 1.5 m string. Feed the string through the glass
tube which has been wrapped with tape Attach a mass hanger to the other end of the string. Spin the
rubber stopper over your head, as demonstrated by your teacher, so that the radius and the speed of the
stopper are both constant. Once these conditions have been attained, have your lab partner(s) time 10
revolutions of the stopper (start counting at zero). Record this time. Repeat this process for different
hanging mass totals. Record all collected and measured data in Table 1.
r
Stopper
Taped Glass Tube
Figure 1. Experimental
setup for measuring the
circular motion of a stopper
attached to a hanging mass
which cause the centripetal
acceleration.
Hanging Mass
Name___________________________
PHY1
Table 1. Data for centriptal acceleration.
Data Collected
Trial
Hanging
Mass (kg)
Time of 10
rev. (s)
Calculations
Period
(s)
2
Speed
(m/s)
Speed
2 2
(m /s )
Acceleration
2
(m/s )
Theoretical
Centripetal
1
Force (N)
Actual
Centripetal
2
Force (N)
1
2
3
4
5
6
7
8
Mass of rubber stopper = ________________kg
Radius of circular path = ___________________m
Example calculations: Show all 5 calculations for Trial 1.
GRAPHS: On separate graph paper, prepare two plots of your data. The first graph should be a plot of the
centripetal force (y axis) versus the speed (x axis) of the stopper. For comparison purposes, plot both the
theoretical and actual centripetal forces using difference colored pencils and connect the data points. The
second graph should be a plot of centripetal force (y axis) versus the square of the stoppers speed (x axis).
Again for comparison purposes, plot both the theoretical and actual centripetal forces using different colored
pens.
Do these plots agree with the Equation 3? Explain your answer using the shapes of your graphs.
1
2
Be sure to use the mass of the stopper in this calculation, F = mV /r, since it is the object that is being
accelerated.
2
The weight of the mass that is haging is what is causing the centripetal acceleration. To do this calculation
2
simply multiply the hanging mass by 9.8 m/s .